Scales of Measurement

Scales of Measurement

The scale indicates the data summarization and statistical analyses that are most appropriate. It determines the amount of information in the data.

Scales of measurement include:

Scales of Measurement

Today, we will explore scales of measurement by creating choropleths using data from the Montana Department of Revenue.¹

Qualitative versus Quantitative data

Data can be qualitative or quantitative.

The appropriate thematic map depends on whether the data for the variable are qualitative or quantitative.

Qualitative Data

Qualitative data indicate what kind.

• Labels or names used to identify an attribute of each element. E.g., Black or white, male or female.
• Often referred to as categorical data
• May use either the nominal or ordinal scale of measurement
• Can be either numeric or non-numeric

Quantitative Data

Quantitative data indicate how many or how much.

• Discrete, if measuring how many. E.g., number of 6-packs consumed at tail-gate party
• Continuous, if measuring how much. E.g., pounds of hamburger consumed at tail-gate party
• Quantitative data are always numeric.
• Ordinary arithmetic operations are meaningful for most quantitative data.

Logical

Logical data are True/False; it is a binary form of nominal data (see next slide!).

• A non-numeric label (true/false) or numeric code (1/0) may be used to represent logical data.
• Many statistical tests, when performed on logical data, yield proportions. For example, taking the mean of a logical variable (with 1 representing true, and 0 representing false) will reveal the proportion of the sample that is “true”.

Nominal

Nominal data are categorically discrete data such as the name of a country visited, type of ground-cover, or the name of a biome.

• This one is easy to remember because nominal sounds like name (they have the same Latin root).
• A non-numeric label or numeric code may be used for nominal data.

Ordinal

Ordinal data are nominal data where the order or rank of the data is meaningful. However, the distance (interval) between categories is unknown or irregular.

• A non-numeric label or numeric code may be used.
• For example: freshmen → sophomore → junior → senior.

Interval

Interval data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure.

• Interval data are always numeric, and may be continuous or discrete.
• Interval data often do not have a zero that represents nothingness; temperature in the Celsius or Fahrenheit scales are examples of Interval data.
• You can add or subtract interval data, but you shouldn’t multiply or divide them.

Ratio

Ratio data have all the properties of interval data and the ratio of two values is meaningful.

• Ratio data are always numeric, and may be continuous or discrete.
• Ratio data must contain a true zero value that indicates that nothing exists for the variable at the zero point.
• Variables such as precipitation, temperature in degrees Kelvin, distance, height, weight, and time use the ratio scale.
• You can add, subtract, multiply and divide ratio scale data.

Cross-sectional Data

Cross-sectional data are observations across individuals at the same point in time, or aggregated over the same time period.

Time Series Data

Time series data are collected over several time periods.